Simplify the following expression: $y = \dfrac{4p^2 - 4p - 168}{p - 7} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $4$ , so we can rewrite the expression: $ y =\dfrac{4(p^2 - 1p - 42)}{p - 7} $ Then we factor the remaining polynomial: $p^2 {-1}p {-42} $ ${-7} + {6} = {-1}$ ${-7} \times {6} = {-42}$ $ (p {-7}) (p + {6}) $ This gives us a factored expression: $\dfrac{4(p {-7}) (p + {6})}{p - 7}$ We can divide the numerator and denominator by $(p + 7)$ on condition that $p \neq 7$ Therefore $y = 4(p + 6); p \neq 7$